* Generalized quantifiers are a special case of operating on continuations. [[!wikipedia Richard_Montague]] analyzed all NPs, including, e.g., proper names, as sets of properties.

This gives names and quantificational NPs the same semantic type, which explain why we can coordinate them (*John and everyone*, *Mary or some graduate student*). So instead of thinking of a name as refering to an individual, which then serves as the argument to a verb phrase, in the Generalized Quantifier conception, the name denotes a higher-order function that takes the verb phrase (its continuation) as an argument. Montague only continuized

one syntactic category (NPs), but a more systematic approach would continuize uniformly throughout the grammar.

-* Computing the meanings of expressions involving focus. Consider the difference in meaning between *John only drinks Perrier*, with main sentence accent on *Perrier*, versus *John only DRINKs Perrier*. Mats Rooth, in his 1995 dissertation, showed how to describe these meanings by having the focussed expression contribute a normal denotation and a focus alternative set denotation. The focus alternative sets had to be propagated upwards through the compositional semantics. One way to implement this idea is by means of delimited continuations, making use of operators similar to fcontrol and run proposed for a scheme-like language by Sitaram and other computer scienticsts. See <http://dx.doi.org/10.1.1.100.9748>.

+* Computing the meanings of expressions involving focus. Consider the difference in meaning between *John only drinks Perrier*, with main sentence accent on *Perrier*, versus *John only DRINKs Perrier*. Mats Rooth, in his 1995 dissertation, showed how to describe these meanings by having the focussed expression contribute a normal denotation and a focus alternative set denotation. The focus alternative sets had to be propagated upwards through the compositional semantics. One way to implement this idea is by means of delimited continuations, making use of operators similar to fcontrol and run proposed for a scheme-like language by Sitaram and other computer scienticsts. See [another paper by CB](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.100.9748&rep=rep1&type=pdf).

* Generalized coordination, as proposed by Partee and Rooth in highly influential papers in the 1980s. The idea is that the way that *John saw Mary or Bill* comes to mean *John saw Mary or John saw Bill* is by cloning the context of the direct object, feeding one of the clones *Mary*, feeding the other clone *Bill*, and disjoining the resulting propositions. See either of the two papers mentioned in the previous two items for discussion.

-* Anaphora, as in *Everyone's mother loves him* (which says that for every person x, x's mother loves x). <http://dx.doi.org/10.1007/s10988-005-6580-7> See also a different implementation of a similar idea in work of [Philippe de Groote](http://ecommons.library.cornell.edu/bitstream/1813/7577/4/salt16_degroote_1_16.pdf).

+* Anaphora, as in *Everyone's mother loves him* (which says that for every person x, x's mother loves x). [A paper by CB and Chung-chieh Shan](http://dx.doi.org/10.1007/s10988-005-6580-7) discusses an implementation in terms of delimited continuations. See also a different implementation in work of [Philippe de Groote](http://ecommons.library.cornell.edu/bitstream/1813/7577/4/salt16_degroote_1_16.pdf).

* As suggested in class, it is possible to think of the side effects of expressives such as *damn* in *John read the damn book* in terms of control operators such as call/cc in Scheme.

At the end of the seminar we gave a demonstration of modeling [[damn]] using continuations...see the [summary](/damn) for more explanation and elaboration. In the meantime, you can read a new paper about this idea [here](http://tinyurl.com/cbarker/barker-bernardi-shan-interaction.pdf)---comments welcome.